Research performed to-date on data assimilation (DA) in storm surge modeling has found it to have limited value for predicting rapid surge responses (e.g., those accompanying tropical cyclones). In this paper, we submit that a well-resolved, barotropic hydrodynamic model is typically able to capture the surge event itself, leaving slower processes that determine the large scale, background water level as primary sources of water level error. These "unresolved drivers" reflect physical processes not included in the model's governing equations or forcing terms, such as far field atmospheric forcing, baroclinic processes, major ocean currents, steric variations, or precipitation. We have developed a novel, efficient, optimal interpolation-based DA scheme, using observations from coastal water level gages, that dynamically corrects for the presence of unresolved drivers. The methodology is applied for Hurricane Matthew (2016) and results demonstrate it is highly effective at removing water level residuals, roughly halving overall surge errors for that storm. The method is computationally efficient, well-suited for either hindcast or forecast applications and extensible to more advanced techniques and datasets.

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Numerical mixing is inevitable for ocean models due to tracer advection schemes. Until now, there is no robust way to identify the regions of spurious mixing in ocean models. We propose a new method to compute the spatial distribution of the spurious diapycnic mixing in an ocean model. This new method is an extension of available potential energy density method proposed by Winters and Barkan (2013). We test the new method in lock-exchange and baroclinic eddies test cases. We can quantify the amount and the location of numerical mixing. We find high-shear areas are the main regions which are susceptible to numerical truncation errors. We also test the new method to quantify the numerical mixing in different horizontal momentum closures. We conclude that Smagorinsky viscosity has less numerical mixing than the Leith viscosity using the same non-dimensional constant.

A simple improvement to objective analysis of hydrographic data is proposed to eliminate spatial aliasing effects in tidally energetic regions. The proposed method consists of the evaluation of anomalies from observations with respect to circulation model fields. The procedure is run iteratively to achieve convergence. The method is applied in the Bay of Fundy and compared with traditional objective analysis procedures and dynamically adjusted climatological fields. The hydrographic skill (difference between observed and model temperature and salinity) of the dynamically adjusted objective analysis is significantly improved by reducing bias and correcting the vertical structure. Representation of the observed velocities is also improved. The resulting flow is consistent with the known circulation in the Bay.